Hybrid simulation of ESD events by SPICE-like and finite-difference time-domain methods

An electron-phonon interaction model is proposed and applied to the transient thermal transport simulation during electrostatic discharge (ESD) event in the NMOS transistor. The high electron energy induced by the ESD in the transistor is transferred to the lattice phonons through electron-phonon interaction in the local region of the transistor. Due to this fact, a hot spot turns up, the size of which is much smaller than the phonon mean free path in the silicon layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied to describe the interactions among different phonon branches and different phonon frequencies. The Joule heating by the electronphonon scattering is modeled through the intervalley and intravalley processes by introducing the average electron energy. In the simulation, the electron-phonon interaction model is used in the hot spot region, and then after a quasi-equilibrium state is achieved there, the temperature of lattice phonons in the silicon is calculated by using the phonon-phonon interaction model. The revolution of peak temperature in the hot spot during the ESD event is simulated and compared to that obtained by the previous full phonon dispersion model which treats the electron-phonon scattering as a volumetric heat source. The results show that the lower group velocity phonon modes (i.e. higher frequency) and optical mode of negligible group velocity obtain the highest energy density from electrons during the ESD event, which induces the devices melting phenomenon. The thermal response of phonon is also investigated, and it is found that the ratio of the phonon group velocity to the phonon specific heat can account for the phonon thermal response. If the ratio is higher than 2, the phonon have a good response to the heat input changes.

Integrated circuits are susceptible to electrostatic discharge (ESD) events. Real-time detection and alerting of ESD events in semiconductor manufacturing environments is the key to achieving well ESD control. Additionally, the magnitude and duration of an ESD event are strongly correlated with the specific type of ESD events. The development of a novel ESD event detector, integrated on a single chip and featuring a logarithmic amplifier, a magnitude discriminator, and a time discriminator, has been motivated by this. This detector has been designed and fabricated in a 0.18-<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>m CMOS process. The magnitude of the ESD event can be detected and converted to 5-bit digital output codes, whereas the time duration of the ESD event can be converted to 3-bit digital output codes by the newly developed ESD event detector. It has been proven in field applications that the detected ESD events can be successfully transmitted to the ESD control center through the RF Wi-Fi module, enabling real-time ESD monitoring and control in manufacturing environments.

New version of FDTD with GFM program in Schwarzschild space–time

Electrostatic Discharge (ESD) events can cause irreversible damage during production, packaging and application of Vertical-Cavity Surface Emitting Lasers (VCSELs). Experimental investigation of those damage patterns inside a real device is a complex and expensive task. Simulation tools can provide insight into the physics during an actual discharge event. This paper aims to analyze ESD events in VCSELs with a microscopic simulation. With the help of a state-of-the art Technology Computer Aided Design (TCAD) virtual ESD tests are performed on oxide-confined VCSELs. The 2-D simulation model takes into account high-field effects and self-heating in a hydrodynamic framework that allows time-dependent spatially resolved monitoring of critical quantities (such as electric field across the oxide, temperature profile, current densities) during the ESD events. Human Body Model (HBM), Machine Model (MM) and Charged Device Model (CDM) show typical local heating and current crowding effects which may lead to irreversible damaging of the device. For slow ESD events the temperature peak is found near the center of the device. Faster pulses show maximum temperature at the interface between oxide and aperture. Physics-based explanations in terms of local electric field, heat generation and heat transport are given. Oxide aperture, thickness and its position relative to the intrinsic region strongly influence self-heating, electric fields, current density profiles and the dielectric breakdown conditions. The impact of those factors on ESD robustness are analyzed and guidelines for robust ESD design in VCSELs are presented.

With the further miniaturization of the GMR heads, the electrostatic discharge (ESD) failure has become the primary reliability issue in manufacturing of these sensors. The Joule heating effect during the ESD events result in both thermal and magnetic damages in GMR heads. In this paper, the thermal response of the GMR read head to the excessive current/voltage during an ESD event is investigated numerically using a 3-D finite element analysis. Unlike the previous studies, the thermal properties of the GMR and Al2O3 gap layers used in the simulation are the experimentally measured values. The temperature-rise in GMR heads under human-body-model (HBM) source current is obtained for a range of GMR dimensions and thermal properties of its constituent materials. The simulation results show that temperature in the GMR element sharply increases as the GMR dimensions are reduced, indicating the future GMR heads are more susceptible to the ESD damages. In addition, thermal properties of the GMR and gap materials play key roles in accurate prediction of the temperature field in GMR head during ESD events.

Electrostatic discharge (ESD) is a physical phenomenon that may destroy electronic components due to its high discharge current that may reach a few amperes in just a few ns. However, another major aspect of ESD is the related high-frequency electromagnetic (E/M) fields radiated by the ESD event. The electronic equipment that is affected by the ESD phenomenon is additionally affected by the induced voltages caused by these E/M fields. This is the reason that the current version of the IEC 61000-4-2 on ESD has a special reference to these fields and the measurement setup. Starting with the classical formulation of these fields, this paper reviews the most popular techniques for calculating the ESD electromagnetic fields while also emphasizing the best methods for minimizing computational effort. There is also a separate section for the measurement techniques that have been applied in research works, whose outcomes could be implemented in the next revision of the IEC 61000-4-2. It is extremely important for the next revision to include these measurement setups and the E/M field sensors because the ESD generators should comply with certain values related to the E/M fields they produce.

The numerical dispersion is one of the main factors to affect the accuracy of the finite-difference time-domain (FDTD) method. It can be easy to be taken for granted that a smaller time step leads to smaller simulation errors. This paper reveals that smaller time steps do not always make more accurate results in FDTD simulations. We analytically investigated how time steps affect the numerical dispersion of two FDTD methods: the leapfrog FDTD(2,2) method and the FDTD(2,4) method. The investigations in this paper show that in the FDTD(2,2) method, a larger time step limited by the Courant-Friedrichs-Lewy (CFL) condition is more helpful to reduce the numerical dispersion error. However, in the FDTD(2,4) method, as the time step grows, the numerical dispersion error decreases at the beginning and then increases. Several numerical examples are carried out to verify our analysis.

The electrostatic discharge (ESD) generator calibration described in IEC 61000-4-2 (2008) only specifies contact mode discharge waveforms for the discharge-into-ground scenario. However, the actual device under test input impedance often differs from a short. To study the effect of different load impedances, a test method for ESD generator discharge under different load impedances is proposed. The method only slightly modifies the present calibration setup. The data show that the peak current variation between different brands of ESD generators for nonshorted load impedances is within the tolerance range given by the standard for the peak current. On the other hand, when performing system-efficient ESD design simulations, the load impedance seen by the ESD generator models is also different than a short. Therefore, the discharge current of a variety of ESD generator models is simulated with different load impedances and compared with ESD generator measurement results, which allows the selection of a suitable ESD generator model.

The Finite-Difference Time-Domain (FDTD) method is used to study the scattering effects of extreme ultraviolet (EUV) mask. It requires significant amounts of memory and computation time as the fine grid size is needed for simulation. Theoretically, the accuracy can be increased as the mesh size is decreased in FDTD simulation. However, it is not easy to get the accurate simulation results for the multilayer (ML) structures by FDTD method. The transmission line theory is used to calculate the equivalent refractive index for EUV mask ML to simulate the ML as one layer of bulk artificial material. The reflectivities for EUV light with the normal incidence and small-angle oblique incidence in the bulk artificial material and EUV mask ML are simulated by FDTD method. The Fresnel's equation is used to evaluate the numerical errors for these FDTD simulations, and the results show good agreement between them. Using the equivalent refractive index material for EUV multilayer mask can reduce the computation time and have the accuracy with tolerable numerical errors. The ML structure with periodic surface roughness is also studied by this method, and it shows that only half of computation time is needed to substitute ML to a bulk equivalent refractive index material in FDTD simulations. This proposed method can accelerate the simulations of EUV mask designs.

A method for analyzing electrostatic discharge (ESD) generators and coupling to equipment under test in the frequency domain is proposed. In ESD generators, the pulses are excited by the voltage collapse across relay contacts. The voltage collapse is replaced by one port of a vector network analyer (VNA). All the discrete and structural elements that form the ESD current pulse and the transient fields are excited by the VNA as if they were excited by the voltage collapse. In such a way, the method allows analyzing the current and field-driven linear coupling without having to discharge an ESD generator, eliminating the risk to the circuit and allowing the use of the wider dynamic range of a network analyzer relative to a real-time oscilloscope. The method is applicable to other voltage-collapse-driven tests, such as electrical fast transient, ultrawideband susceptibility testing but requires a linear coupling path.

The finite difference time domain (FDTD) method has been proposed and used for sound field simulation. To reproduce actual sound wave propagation in sound field simulations, it is necessary to apply the radiation characteristics. With the FDTD method, radiation characteristics can be applied by setting sound pressure in a dense grid arrangement. However, conventional techniques for capturing radiation characteristics use a sparse array of microphones and are considered insufficient for the FDTD simulation. Furthermore, the technique required to apply captured acoustic signals in a dense grid arrangement with the FDTD method has not been considered. In this paper, we propose a novel hardware and software system that captures the radiation characteristics for a dense grid arrangement and applies them to the FDTD method, while controlling the sound wave propagation with the non-propagation region. The proposed system produces the average differences from measured values of sound pressure, propagation time, center frequency, and log-spectral distortion of 1.8 dB, 0.04 ms, 700 Hz, and 3.5 dB, respectively, which is more accurate than the conventional techniques. The result shows that this system is useful for improving the accuracy of sound wave propagation reproduction with the sound field simulation.

We study the effect of electrostatic discharge (ESD) on coaxial cable connections between different systems. These cables may be a very efficient entrypoint for unwanted ESD signals. The effect of an electrostatic discharge on the cable shielding is compared to the effect of indirect and direct ESD on the system shielding itself. To study the effect of the various pathways of ESD we use an FDTD algorithm. The disturbance induced in the inside of the cable is evaluated by using the transfer impedance of the cable shield.

The electrostatic discharge (ESD) effect is widely known as a main cause of damage in giant magnetoresistance (GMR) heads (Wallash and Kim, 1995). The transient current may strike the GMR head directly by passing the leads (Li-Yan Zhu, 1999) and this may be prevented by shunting the GMR leads (Bajorek et al, 1995). However, after completing the head gimbal assembly (HGA) production, the shunt leads have to be trimmed in order to test its electrical characteristics. This is thought to cause the ESD effect while trimming the shunt tab of a GMR head, and is investigated here.

In a discharge between charged metal spheres, the effect of the metal spheres on the generated electromagnetic field has not been clearly indicated. One of the authors (Fujiwara) has proposed the following computation method (called the image dipole method) for a spark discharge between metal spheres. The surface of the metal sphere is replaced by an infinite number of image charge pairs, which are arranged so that the surface is kept at the same potential. Then, the generated electromagnetic field is calculated analytically by superposition of the dipole fields caused by the spark current derived from the Rompe‐Weizel spark‐resistance law. It has been shown by the analysis that the metal sphere increases the field level. Then, the electromagnetic field generated by the spark discharge between metal spheres is calculated numerically by the finite‐difference time‐domain (FDTD) method, with the spark current as an excitation source for the metal sphere. The validity of the approach has been shown through comparison to the analytic solution by the image dipole method for the magnetic field waveform.However, the above computation method has the problem that the static electric field before the onset of the discharge cannot be calculated, which makes it difficult to understand fully the ESD field produced by the charged metal bodies. In this paper, the generated electromagnetic field is calculated by the FDTD method (voltage source method), with the spark voltage derived from the spark‐resistor law as an excitation source. The result is compared to the results of calculations by the image dipole method and the current source method. It is shown that the waveform of the electrostatic field cannot be calculated by the current source method, but the voltage source method can calculate the field as in the case of the image dipole method. It is also seen that the magnetic field waveforms obtained by any calculation almost completely agree. The magnetic field waveform generated in the discharge experiment between metal spheres is observed by using a shielded magnetic field probe and a wideband oscilloscope (bandwidth 1.5 GHz), and is shown to agree almost completely with the results of calculations by the voltage source method and the image dipole method. © 2003 Wiley Periodicals, Inc. Electron Comm Jpn Pt 1, 86(7): 54–63, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecja.1169

Electrostatic discharge (ESD) is a source of electromagnetic disturbance. For an ESD immunity test, IEC 61000-4-2 is standardized. In the standard, the air discharge and contact discharge method are described for the application of ESD to equipment under test. Air discharge, which is most common in the field, is a more severe test than contact discharge. Air discharge is dependent on the humidity, the speed of approach to grounded material, the structure of the ESD generator, and so on. An ESD event while charged material approaches grounded material has a more significant effect on electronic equipment than an ESD event from stationary charged material with the same charge potential. This peculiar phenomenon is considered because the rise time becomes faster and the peak spark current becomes larger, but is not well understood for reasons such as the difficulty of reproducibility. To promote an understanding of the spark discharge that occurs while a charged material is approaching a grounded material, the effect of change in the time of the charging voltage on the spark discharge from a stationary metal disk was measured. The experiment showed that the spark voltage and peak spark current increased with a change in the time of the charging voltage, and that the amplitude of the spark current spectra also increased with a change in the time of the charging voltage. The experimental results are considered in terms of the sparking resistance formula, and can be explained qualitatively in terms of the increase of spark voltage. 2010 Wiley Periodicals, Inc. Electr Eng Jpn, 173(3): 1–9, 2010; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/eej.20991